On the spectrum of the algebra of bounded-type symmetric analytic functions on ℓ 1 $\ell _1$

Abstract

We obtain a complete description of the spectrum of the Fréchet algebra of symmetric analytic functions bounded on balls on the sequence space ${\ell }_1$. This is achieved after proving that on the analogous algebra for ${\ell }_p$, $1\le p<\infty$, the radius function of any evaluation homomorphism ${\delta }_x,x\in {\ell }_p$, coincides with the norm of $x$.